✦ LIBER ✦

Direct and Inverse Methods in Nonlinear Evolution Equations: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999

✍ Scribed by Robert Conte

Book ID: 127428811
Publisher: Springer
Year: 2003
Tongue: English
Weight: 1 MB
Series: Lecture Notes in Physics 632
Edition: 1
Category: Library
City: Berlin; New York
ISBN-13: 9783540200871
ISSN: 0075-8450
DOI: 10.1007/b13714

No coin nor oath required. For personal study only.

✦ Synopsis

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities � la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.

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